1  On the pair of opposite surfaces, a solid cube has been painted Yellow, Blue and Black. The cube is then cut into 36 smaller cubes such that 32 cubes are of the same size while remaining are of bigger. And remember no face of any of the bigger cubes is painted blue.
How many cubes have at least one of their faces painted blue?

2  A cube is having three adjacent faces of blue colour. Then it cut once horizontally and once vertically to form cuboids of equal size. Each of thease cuboids is coloured pink on all the uncoloured faces. Then it cut as before in to four cuboid of equal size.
How many cuboids have three faces coloured blue?

3  A task is given to paint a cubical box with six different colours for different faces of the cube.An account of this details are as below :
a. Green face should be adjacent to silver face.
b. Brown face should face down.
c. Red face should lie between yellow and brown faces.
d. Pink face should lie adjacent to Green face.
e. Yellow face should lie opposite to the Brown one.
f. Silver and Pink faces should lie opposite to each other.
The faces adjacent to Green are

4  Consider a cube of having dimensions 4cm*3cm*3cm. On the pair of opposite surfaces of having dimensions 4cm*3cm, the block is painted as yellow. Remaining two opposite surfaces of dimensions 4cm*3cm are painted red. And two surfaces of dimensions 3cm*3cm are painted with green colours. now the black is divided among smaller cubes of dimensions (1cm*1cm*1cm).
How many cubes will have no surface painted?

5  Consider a solid cube of having each side of 8cms. And it is painted as red, blue and black on pairs of opposite faces. Then it is cut in to cubical blocks of each side 2cm. On this information answer the following question.
How many cubes have two faces painted red and black and all other faces unpainted?

6  Consider a cube of having dimensions 4cm*3cm*3cm. On the pair of opposite surfaces of having dimensions 4cm*3cm, the block is painted as yellow. Remaining two opposite surfaces of dimensions 4cm*3cm are painted red. And two surfaces of dimensions 3cm*3cm are painted with green colours. now the black is divided among smaller cubes of dimensions (1cm*1cm*1cm).
How many cubes will have at least one surface painted?

7  Consider a solid pile of dimensions 5*5*5. One hundred and twenty five small cubes of equal size are arranged in same solid pile. Then from one corner one cube is removed from the top. From the opposite corner eight cubes of dimensions 2*2*2 are removed. From third corner a coloumn of three cubes and from the fourth corner a column of four cubess are removed. the remaining solid is coloured red on all the exposed faces. Now on this information answer the following question.
How many cubes have three coloured faces each?

8  Consider a cube is coloured on one face, pink on the opposite face, brown on one face and silver on a face adjacent to the brown face. The other two faces are left uncoloured. It is then cut into 125 smaller cubes of equal size. Now, answer the following question based on the above statements.
How many cubes are coloured silver on one face, orange or pink on another face and have four uncoloured faces?

9  Consider a cuboid of having dimensions 6cm*4cm*1cm. It is painted black on both the surfaces of dimensions (4cm*1cm), green on the surfaces of dimensions (6cm*4cm) and red on the surface of dimensions (6cm*1cm). Now the block is divided into various small cubes of side 1cm. each. The smaller cubes so obtained are separated.
How many cubes will have two sides with green colour and remaining sides without any colour?

10  Consider a solid pile of dimensions 5*5*5. One hundred and twenty five small cubes of equal size are arranged in same solid pile. Then from one corner one cube is removed from the top. From the opposite corner eight cubes of dimensions 2*2*2 are removed. From third corner a coloumn of three cubes and from the fourth corner a column of four cubess are removed. The remaining solid is coloured red on all the exposed faces. Now on this information answer the following question.
How many cubes in the third layer have at least two coloured face each?
